1. Field of the Invention
The present invention relates to optical fibres and, in particular, but not exclusively, to photonic crystal fibres that guide light by virtue of a photonic band-gap.
2. Description of the Related Art
A photonic crystal is a dielectric structure with a refractive index that varies periodically in space, with a period of the order of an optical wavelength. Such a structure has a photonic stop band if light cannot propagate (in any state of polarisation) for certain values of frequency and direction; Bragg diffraction takes place. If the stop band persists for all directions at a given frequency, the light cannot propagate at all and the photonic crystal has a full photonic band-gap; hereinafter referred to simply as a band-gap.
Prior to about 1995, most reports relating to two-dimensional (2-D) photonic crystals invariant in the third dimension (the longitudinal, or z, direction) were associated with so-called ‘in-plane’ band-gaps, in which light was restricted to the transverse plane; having no component in the z-direction so that the propagation constant β=0.
An example of a 2-D photonic crystal is a regular array of rods of one refractive index surrounded by a material with a different refractive index. The rods can, for example, be air columns in a solid material or solid columns of material surrounded by air or another solid material.
When light propagation is restricted to the transverse plane (in-plane), an in-plane 2-D band-gap can appear for a large refractive index contrast, typically in excess of 2.6, where refractive index contrast is defined herein as the ratio of high refractive index to low refractive index. Conveniently, in a two-material system, when the low refractive index material is air, or a vacuum, and the high refractive index material defines the structure, refractive index contrast is the same as the refractive index of the matrix material. Materials commonly used in photonic crystals are gallium arsenide or gallium aluminium arsenide, having refractive indices of around 3.6 and 3.45 respectively, and air, where increasing the refractive index contrast increases the band-gap bandwidth.
In “Full 2-D photonic band-gaps in silica/air structures”, Birks et al., Electronics Letters, 26 Oct. 1995, Vol. 31, No. 22, pp. 1941–1942, it was reported that a full band-gap may be created in a 2-D photonic crystal when there is a propagation component in the longitudinal direction (out-of-plane). It was also reported that this could be achieved with a much lower refractive index contrast, for example around 1.45, than for an in-plane band-gap. In particular it was reported that a full out-of-plane 2-D band-gap could be produced in a silica-air system, where round air columns are arranged in a silica matrix in a hexagonal array. The authors went on to propose a radically new kind of optical fibre, having a hollow core region surrounded by a 2-D band-gap cladding structure, in which light would be confined to the core by the band-gap cladding structure.
Since this paper was published, several groups, including the authors of the paper, have made and reported practical band-gap fibres of the kind proposed by Birks et al.
The first practical band-gap fibre was reported in “Photonic Band Gap Guidance in Optical Fibres”, Knight et al., 20 Nov. 1998, Vol. 282, Science, pp. 1476–1478. The fibre reported in this paper guided light by virtue of a band-gap, which confined the light to a small region of silica around a hollow air core. This paper demonstrated for the first time that light guidance could be performed by using a band-gap, associated with a 2-D photonic crystal structure, along an optical fibre. In this case, guidance was not in an air core.
The first band-gap fibre to guide light in an air core was reported in “Single-mode photonic band-gap guidance of light in air”, Cregan et al., Science, Vol. 285, pp 1537–1539, 3 Sep. 1999. That this publication was not made until nearly four years after air-core-guidance in band-gap fibres were first predicted is an indication of the difficulties associated with making such a fibre. The reported fibre had a cladding, generally comprising a triangular lattice of air holes in a silica matrix, surrounding a core region having a size approximately equal to seven unit cells; a middle unit cell and the surrounding six unit cells.
In “Analysis of air-guiding photonic band-gap fibres”, Broeng et al., Optics Letters, Vol. 25, No. 2, pp. 96–98, Jan. 15, 2000, the authors provided a theoretical analysis of an air-guiding, silica and air band-gap fibre. The band-gap fibre had a cladding defined by a triangular lattice of round air holes, which amounted to 70% by volume of the cladding structure, and a seven-cell core defect having a radius of √7Λ/2 (where Λ is the lattice pitch of the cladding). The authors applied a variational method for solving the vectorial magnetic wave equation as an eigenvalue problem to analyse the band-gap structure. For a fixed out-of-plane wave-vector component β, a band diagram was generated that showed that, for a normalised propagation constant βΛ=9.0, a band-gap appeared at around a normalised frequency kΛ of 9.0. This band-gap is seen to exist between the fourth and fifth photonic bands of the band diagram and was said to be the lowest frequency band-gap of the band-gap structure, although other band-gaps were said to exist, at least for other structures.
In the chapter entitled “Photonic Crystal Fibers: Effective Index and Band-Gap Guidance” from the book “Photonic Crystal and Light Localization in the 21st Century”, C. M. Soukoulis (ed.), ©2001 Kluwer Academic Publishers, the authors presented a useful overview of photonic crystal fibre technology. The chapter includes a description of a band structure for a triangular lattice of air holes, defined by a high dielectric material (∈=13), and a description of a band structure for a similar, silica and air structure having a seven-cell air-core defect (comparable with the structure in the preceding Broeng et al. paper).
Although the loss of practical band-gap fibres has decreased significantly since the idea was first proposed, see, for example, “Low Loss (13 dB/km) Air Core Photonic Band-Gap Fibre”, Venkataraman et al., Post Deadline Session 1:PD1.1, ECOC 2002, the underlying design of reported band-gap fibres has not significantly changed. For example, the fibre reported in the aforementioned paper had a cladding structure formed from a silica matrix defining a triangular lattice of air-holes surrounding a core region, which is the size of about seven unit cells (each centred on a hole); a middle unit cell and the surrounding six unit cells. The main difference between this fibre and earlier fibres is that the cladding holes in the more recent fibres are larger, causing the cladding regions to have a higher fraction by volume of air.
In the paper “All silica photonic band-gap fiber”, Riishede et al. CLEO 2003, paper CTuC5, the authors extended the theory first reported in the Birks et al. paper referred to previously herein. The authors reported that it is possible to make a band-gap fibre in which the band-gap is produced by an array of Ge-doped silica rods supported in a matrix of lower refractive index, un-doped silica. A core region of the fibre was also made of un-doped silica. The refractive index contrast in the reported fibre was extremely low, at around 1.45:1.47. In fact, the authors reported that they were able to produce full 2-D out-of-plane band-gaps with refractive index contrasts lower than one percent. This paper is significant in that it further distinguishes the theory of in-plane band-gaps, requiring a high refractive index contrast, from the theory of out-of-plane band-gaps.